Integer-reversible transform, in particular the Integer MDCT (IntMDCT), is used in lossless or HD (high definition) audio/video coding. For example, the recently standardised MPEG-4 SLS codec uses an IntMDCT.
The approach may be applicable as well in other fields where lossless transformations are used. E.g., integer-reversible Wavelet transforms are used for lossless image and video coding.
The problem of any integer-reversible transformation is that the transformation is split into consecutive steps, each of which introduces considerable rounding errors to the signal. This problem gets more significant the lower the level of the useful signal to be encoded. Therefore, the rounding error noise is a limiting factor in residual coding schemes, in which the residuum is the error signal between the original (or lossless or HD) signal and the lossy or standard definition coded version of it.
Without noise shaping the rounding error noise will impact all frequency bins of the transformed signal equally. This is a particular problem for frequency bins in which the actual signal level is low. In bins in which the rounding error gets dominant, a large ‘penalty’ in terms of strongly increased entropy (and thus data rate) is to be paid for the lossless transformation. The penalty is much lower for frequency bins where the rounding errors are not dominant.